SOLUTION: the sides of a rhombus measure 12 inches and one of the acute angles measures 50 degrees. find the lengths of the diagonals to the nearest integer

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Question 862824: the sides of a rhombus measure 12 inches and one of the acute angles measures 50 degrees. find the lengths of the diagonals to the nearest integer
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
This is maybe a long way to get to one of the diagonals; but this rhombus is like two isosceles triangles, with one angle 50 degree, therefore the two equal angles 20 degree each, and the equal legs are 12 inches each. You can use Law of Cosines to find the diagonal which serves as the base side opposite the 50 degree angle.

12%5E2%2B12%5E2-2%2A12%2A12%2Acos%2850%29=d, and letting d be the diagonal. There might be a method NOT using Trigonometry, but I can't think of what exactly it is. Possibly checking a high school level Geometry textbook would show it. Still, the Law of Cosines idea should be fundamentally sensible.